<p>The bending fracture problem of a micro-/nanoscale elastic thin plate containing through-thickness collinear periodic cracks is investigated in this paper. Based on the classical thin plate theory and Gurtin–Murdoch surface elasticity theory, the collinear through-thickness crack problem can be transformed into a mixed boundary value problem. By making use of the corresponding boundary conditions and the Fourier transform technique, the problem is converted to solving a singular integral equation. The closed-form solutions of singular internal fields including the moments and shear forces are determined for a cracked thin plate with surface elasticity subjected to constant moments on the crack faces. The moment or stress intensity factors at the crack tips have an inverse square-root singularity. Numerical examples show that the singular fields and their intensity factors are significantly influenced by surface properties, plate thickness, and the spacing between adjacent cracks.</p>

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Bending fracture of a microscale elastic thin plate with through-thickness collinear periodic cracks

  • Zhen-Liang Hu,
  • Fei Long,
  • Xue-Yang Zhang,
  • Xian-Fang Li

摘要

The bending fracture problem of a micro-/nanoscale elastic thin plate containing through-thickness collinear periodic cracks is investigated in this paper. Based on the classical thin plate theory and Gurtin–Murdoch surface elasticity theory, the collinear through-thickness crack problem can be transformed into a mixed boundary value problem. By making use of the corresponding boundary conditions and the Fourier transform technique, the problem is converted to solving a singular integral equation. The closed-form solutions of singular internal fields including the moments and shear forces are determined for a cracked thin plate with surface elasticity subjected to constant moments on the crack faces. The moment or stress intensity factors at the crack tips have an inverse square-root singularity. Numerical examples show that the singular fields and their intensity factors are significantly influenced by surface properties, plate thickness, and the spacing between adjacent cracks.